The facet ideal of a simplicial complex
Commutative Algebra
2007-05-23 v1 Combinatorics
Abstract
To a simplicial complex, we associate a square-free monomial ideal in the polynomial ring generated by its vertex set over a field. We study algebraic properties of this ideal via combinatorial properties of the simplicial complex. By generalizing the notion of a tree from graphs to simplicial complexes, we show that ideals associated to trees satisfy sliding depth condition, and therefore have normal and Cohen-Macaulay Rees rings. We also discuss connections with the theory of Stanley-Reisner rings.
Cite
@article{arxiv.math/0210110,
title = {The facet ideal of a simplicial complex},
author = {Sara Faridi},
journal= {arXiv preprint arXiv:math/0210110},
year = {2007}
}
Comments
To appear in Manuscripta Mathematica